Why would handling a dead, bleeding, rabid animal pose a problem? Rabies is not spread through blood contact.
Rabies is a rare virus that can be transmitted to humans from animals just like any other virus that humans are susceptible to. Open wounds, wiping the eyes with the saliva of the animal, etc....
But most importantly, any animal that is killed because it is suspected of having rabies is required to be turned over to the state for examination to determine that it is rabies infected.......